Organization of Results

Currently, complete or nearly complete coverage of results from sampling, optimization and calibration methods, parameter studies, and stochastic expansions exists. Coverage will continue to expand in future releases to include not only the results of all methods, but other potentially useful information such as interface evaluations and model tranformations.

Methods in Dakota have a character string Id and are executed by Dakota one or more times. (Methods are executed more than once in studies that include a nested model, for example.) The Id may be provided by the user in the input file using the id_method keyword, or it may be automatically generated by Dakota. Dakota uses the label NO_METHOD_ID for methods that are specified in the input file without an id_method, and NOSPEC_METHOD_ID_<N> for methods that it generates for its own internal use. The <N> in the latter case is an incrementing integer that begins at 1.

The results for the <N>th execution of a method that has the label <method Id> are stored in the group

/methods/<method Id>/results/execution:<N>/

The /methods group is always present in Dakota HDF5 files, provided at least one method added results to the output. (In a future Dakota release, the top level groups /interfaces and /models will be added.) The group execution:1 also is always present, even if there is only a single execution.

The groups and datasets for each type of result that Dakota is currently capable of storing are described in the following sections. Every dataset is documented in its own table. These tables include:

• A brief description of the dataset.

• The location of the dataset relative to /methods/<method Id>/execution:<N>. This path may include both literal text that is always present and replacement text. Replacement text is <enclosed in angle brackets and italicized>. Two examples of replacement text are <response descriptor> and <variable descriptor>, which indicate that the name of a Dakota response or variable makes up a portion of the path.

• Clarifying notes, where appropriate.

• The type (String, Integer, or Real) of the information in the dataset.

• The shape of the dataset; that is, the number of dimensions and the size of each dimension.

• A description of the dataset’s scales, which includes - The dimension of the dataset that the scale belongs to. - The type (String, Integer, or Real) of the information in the scale. - The label or name of the scale. - The contents of the scale. Contents that appear in plaintext are literal and will always be present in a scale. Italicized text describes content that varies. - notes that provide further clarification about the scale.

• A description of the dataset’s attributes, which are key:value pairs that provide helpful context for the dataset.

The Expected Output section of each method’s keyword documentation indicates the kinds of output, if any, that method currently can write to HDF5. These are typically in the form of bulleted lists with clariying notes that refer back to the sections that follow.

Study Metadata

Several pieces of information about the Dakota study are stored as attributes of the top-level HDF5 root group (“/”). These include:

Label	Type	Description
dakota_version	String	Version of Dakota used to run the study
dakota_revision	String	Dakota version control information
output_version	String	Version of the output file
input	String	Dakota input file
top_method	String	Id of the top-level method
total_cpu_time	Real	Combined parent and child CPU time in seconds
parent_cpu_time	Real	Parent CPU time in seconds (when Dakota is built with UTILIB)
child_cpu_time	Real	Child CPU time in seconds (when Dakota is built with UTILIB)
total_wallclock_time	Real	Total wallclock time in seconds (when Dakota is built with UTILIB)
mpi_init_wallclock_time	Real	Wallclock time to MPI_Init in seconds (when Dakota is built with UTILIB and run in parallel)
run_wallclock_time	Real	Wallclock time since MPI_Init in seconds (when Dakota is built with UTILIB and run in parallel)
mpi_wallclock_time	Real	Wallclock time since MPI_Init in seconds (when Dakota is not built with UTILIB and run in parallel)

A Note about Variables Storage

Variables in most Dakota output (e.g. tabular data files) and input (e.g. imported data to construct surrogates) are listed in “input spec” order. (The variables keyword section is arranged by input spec order.) In this ordering, they are sorted first by function:

1. Design

2. Aleatory

3. Epistemic

4. State

And within each of these categories, they are sorted by domain:

1. Continuous

2. Discrete integer (sets and ranges)

3. Discrete string

4. Discrete real

A shortcoming of HDF5 is that datasets are homogeneous; for example, string- and real-valued data cannot readily be stored in the same dataset. As a result, Dakota has chosen to flip “input spec” order for HDF5 and sort first by domain, then by function when storing variable information. When applicable, there may be as many as four datasets to store variable information: one to store continuous variables, another to store discrete integer variables, and so on. Within each of these, variables will be ordered by function.

Sampling Moments

sampling produces moments (e.g. mean, standard deviation or variance) of all responses, as well as 95% lower and upper confidence intervals for the 1st and 2nd moments. These are stored as described below. When sampling is used in incremental mode by specifying refinement_samples, all results, including the moments group, are placed within groups named increment:<N>, where <N> indicates the increment number beginning with 1.

	Moments
Description	1st through 4th moments for each response
Location	[increment:<N>]/moments/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: length of 4
Type	Real
Scales	Dimension Type Label Contents Notes 0 String moments mean, std_deviation, skewness, kurtosis Only for standard moments 0 String moments mean, variance, third_central, fourth_central Only for central moments

	Moment Confidence Intervals
Description	Lower and upper 95% confidence intervals on the 1st and 2nd moments
Location	moment_confidence_intervals/<response descriptor>
Shape	2-dimensional: 2x2
Type	Real
Scales	Dimension Type Label Contents Notes 0 String bounds lower, upper 1 String moments mean, std_deviation Only for standard moments 1 String moments mean, variance Only for central moments

Correlations

A few different methods produce information about the correlations between pairs of variables and responses (collectively: factors). The four tables in this section describe how correlation information is stored. One important note is that HDF5 has no special, native type for symmetric matrices, and so the simple correlations and simple rank correlations are stored in dense 2D datasets.

	Simple Correlations
Description	Simple correlation matrix
Location	[increment:<N>]/simple_correlations
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	2-dimensional: number of factors by number of factors
Type	Real
Scales	Dimension Type Label Contents Literal_contents Notes 0, 1 String factors Variable and response descriptors false The scales for both dimensions are identical

	Simple Rank Correlations
Description	Simple rank correlation matrix
Location	[increment:<N>]/simple_rank_correlations
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	2-dimensional: number of factors by number of factors
Type	Real
Scales	Dimension Type Label Contents Literal_contents Notes 0, 1 String factors Variable and response descriptors false The scales for both dimensions are identical

	Partial Correlations
Description	Partial correlations
Location	[increment:<N>]/partial_correlations/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of variables
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable descriptors false

	Partial Rank Correlations
Description	Partial Rank correlations
Location	[increment:<N>]/partial_rank_correlations/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of variables
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable descriptors false

Probability Density

Some aleatory UQ methods estimate the probability density of resposnes.

	Probability Density
Description	Probability density of a response
Location	[increment:<N>]/probability_density/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of bins in probability density
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Real lower_bounds Lower bin edges false 0 Real upper_bounds Upper bin edges false

Level Mappings

Aleatory UQ methods can calculate level mappings (from user-specified probability, reliability, or generalized reliability to response, or vice versa).

	Probability Levels
Description	Response levels corresponding to user-specified probability levels
Location	[increment:<N>]/probability_levels/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of requested levels for the response
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Real probability_levels User-specified probability levels false

	Reliability Levels
Description	Response levels corresponding to user-specified reliability levels
Location	[increment:<N>]/reliability_levels/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of requested levels for the response
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Real reliability_levels User-specified reliability levels false

	Generalized Reliability Levels
Description	Response levels corresponding to user-specified generalized reliability levels
Location	[increment:<N>]/gen_reliability_levels/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of requested levels for the response
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Real gen_reliability_levels User-specified generalized reliability levels false

	Response Levels
Description	Probability, reliability, or generalized reliability levels corresponding to user-specified response levels
Location	[increment:<N>]/response_levels/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	1-dimensional: number of requested levels for the response
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Real response_levels User-specified response levels false

Variance-Based Decomposition (Sobol’ Indices)

Dakota’s sampling method can produce main and total effects; stochastic expansions ( polynomial_chaos, stoch_collocation ) additionally can produce interaction effects.

	Main Effects
Description	First-order Sobol’ indices
Location	main_effects/<response descriptor>
Shape	1-dimensional: number of variables
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable descriptors false

	Total Effects
Description	Total-effect Sobol’ indices
Location	total_effects/<response descriptor>
Shape	1-dimensional: number of variables
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable descriptors false

Each order (pair, 3-way, 4-way, etc) of interaction is stored in a separate dataset. The scales are unusual in that they are two-dimensional to contain the labels of the variables that participate in each interaction.

	Interaction Effects
Description	Sobol’ indices for interactions
Location	order_<N>_interactions/<response descriptor>
Shape	1-dimensional: number of Nth order interactions
Type	Real
Scales	Dimension Type Label Contents Literal_contents Notes 0 String variables Descriptors of the variables in the interaction false Scales for interaction effects are 2D datasets with the dimensions (number of interactions, N)

Integration and Expansion Moments

Stochastic expansion methods can obtain moments two ways.

	Integration Moments
Description	Moments obtained via integration
Location	integration_moments/<response descriptor>
Shape	4
Type	Real
Scales	Dimension Type Label Contents Literal_contents Notes 0 String moments mean, std_deviation, skewness, kurtosis Only for standard moments 0 String moments mean, variance, third_central, fourth_central true Only for central moments

	Expansion Moments
Description	Moments obtained via expansion
Location	expansion_moments/<response descriptor>
Shape	4
Type	Real
Scales	Dimension Type Label Contents Literal_contents Notes 0 String moments mean, std_deviation, skewness, kurtosis Only for standard moments 0 String moments mean, variance, third_central, fourth_central true Only for central moments

Extreme Responses

sampling with epistemic variables produces extreme values (minimum and maximum) for each response.

	Extreme Responses
Description	The sample minimum and maximum of each response
Location	[increment:<N>]/extreme_responses/<response descriptor>
Notes	The [increment:<N>] group is present only for sampling with refinement
Shape	2
Type	Real
Scales	Dimension Type Label Contents 0 String extremes minimum, maximum

Parameter Sets

All parameter studies ( vector_parameter_study, list_parameter_study, multidim_parameter_study, centered_parameter_study ) record tables of evaluations (parameter-response pairs), similar to Dakota’s tabular output file. Centered parameter studies additionally store evaluations in an order that is more natural to intepret, which is described below.

In the tabular-like listing, variables are stored according to the scheme described in a previous section.

	Parameter Sets
Description	Parameter study evaluations in a tabular-like listing
Location	parameter_sets/{continuous_variables, discrete_integer_variables, discrete_string_variables, discrete_real_variables, responses}
Shape	2-dimensional: number of evaluations by number of variables or responses
Type	Real, String, or Integer, as applicable
Scales	Dimension Type Label Contents Literal_contents 1 String variables or responses Variable or response descriptors false

Variable Slices

Centered paramter studies store “slices” of the tabular data that make evaluating the effects of each variable on each response more convenient. The steps for each individual variable, including the initial or center point, and corresponding responses are stored in separate groups.

	Variable Slices
Description	Steps, including center/initial point, for a single variable
Location	variable_slices/<variable descriptor>/steps
Shape	1-dimensional: number of user-specified steps for this variable
Type	Real, String, or Integer, as applicable

	Variable Slices - Responses
Description	Responses for variable slices
Location	variable_slices/<variable descriptor>/responses
Shape	2-dimensional: number of evaluations by number of responses
Type	Real
Scales	Dimension Type Label Contents Literal_contents 1 String responses Response descriptors false

Best Parameters

Dakota’s optimization and calibration methods report the parameters at the best point (or points, for multiple final solutions) discovered. These are stored using the scheme decribed in the variables section. When more than one solution is reported, the best parameters are nested in groups named set:<N>, where <N> is a integer numbering the set and beginning with 1.

State (and other inactive variables) are reported when using objective functions and for some calibration studies. However, when using configuration variables in a calibration, state variables are suppressed.

	Best Parameters
Description	Best parameters discovered by optimization or calibration
Location	[set:<N>]/best_parameters/{continuous, discrete_integer, discrete_string, discrete_real}
Notes	The [set:<N>] group is present only when multiple final solutions are reported.
Shape	1-dimensional: number of variables
Type	Real, String, or Integer, as applicable
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable descriptors false

Best Objective Functions

Dakota’s optimization methods report the objective functions at the best point (or points, for multiple final solutions) discovered. When more than one solution is reported, the best objective functions are nested in groups named set:<N>, where <N> is a integer numbering the set and beginning with 1.

	Best Objective Functions
Description	Best objective functions discovered by optimization
Location	[set:<N>]/best_objective_functions
Notes	The [set:<N>] group is present only when multiple final solutions are reported.
Shape	1-dimensional: number of objective functions
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String responses Response descriptors false

Best Nonlinear Constraints

Dakota’s optimization and calibration methods report the nonlinear constraints at the best point (or points, for multiple final solutions) discovered. When more than one solution is reported, the best constraints are nested in groups named set:<N>, where N is a integer numbering the set and beginning with 1.

	Best Nonlinear Constraints
Description	Best nonlinear constraints discovered by optimization or calibration
Location	[set:<N>]/best_constraints
Notes	The [set:<N>] group is present only when multiple final solutions are reported.
Shape	1-dimensional: number of nonlinear constraints
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String responses Response descriptors false

Calibration

When using calibration terms with an optimization method, or when using a nonlinear least squares method such as nl2sol, Dakota reports residuals and residual norms for the best point (or points, for multiple final solutions) discovered.

	Best Residuals
Description	Best residuals discovered
Location	best_residuals
Shape	1-dimensional: number of residuals
Type	Real

	Best Residual Norm
Description	Norm of best residuals discovered
Location	best_norm
Shape	Scalar
Type	Real

Parameter Confidence Intervals

Least squares methods (nl2sol, nlssol_sqp, optpp_g_newton) compute confidence intervals on the calibration parameters.

	Parameter Confidence Intervals
Description	Lower and upper confidence intervals on calibrated parameters
Location	confidence_intervals
Notes	The confidence intervals are not stored when there is more than one experiment.
Shape	2-dimensional: 2x2
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable desriptors false 1 String bounds lower, upper

Best Model Responses (without configuration variables)

When performing calibration with experimental data (but no configruation variables), Dakota records, in addition to the best residuals, the best original model resposnes.

	Best Model Responses
Description	Original model responses for the best residuals discovered
Location	best_model_responses
Shape	1-dimensional: number of model responses
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String responses Response descriptors false

Best Model Responses (with configuration variables)

When performing calibration with experimental data that includes configuration variables, Dakota reports the best model responses for each experiment. These results include the configuration variables, stored in the scheme described in the variables section, and the model responses.

	Best Configuration Variables for Experiment
Description	Configuration variables associated with experiment N
Location	best_model_responses/experiment:<N>/{continuous_config_variables, discrete_integer_config_variables, discrete_string_config_variables, discrete_real_config_variables}
Shape	1-dimensional: number of variables
Type	Real, String, or Integer, as applicable
Scales	Dimension Type Label Contents Literal_contents 0 String variables Variable descriptors false

	Best Model Responses for Experiment
Description	Original model responses for the best residuals discovered
Location	best_model_responses/experiment:<N>/responses
Shape	1-dimensional: number of model responses
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 String responses Response descriptors false

Multistart and Pareto Set

The multi_start and pareto_set methods are meta-iterators that control multiple optimization sub-iterators. For both methods, Dakota stores the results of the sub-iterators (best parameters and best results). For multi_start, Dakota additionally stores the initial points, and for pareto_set, it stores the objective function weights.

	Starting Points (multi_start)
Description	Starting points for multi_start
Location	starting_points/continuous
Notes	Currently only continuous starting points are supported by multi_start
Shape	2-dimensional: number of sets by number of variables
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Integer set_ids set Ids false 1 String variables Variable descriptors false

	Weights (pareto_set)
Description	Response Weights for pareto_set
Location	weights
Shape	2-dimensional: number of sets by number of responses
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Integer set_ids set Ids false 1 String weights w1, w2, … wN true

	Best Parameters (multi_start or pareto_set)
Description	Best parameters discovered by multi_start or pareto_set
Location	best_parameters/{continuous, discrete_integer, discrete_string, discrete_real}
Shape	2-dimensional: number of sets by number of variables
Type	Real, String, or Integer, as applicable
Scales	Dimension Type Label Contents Literal_contents 0 Integer set_ids set Ids false 1 String variables Variable descriptors false

	Best responses
Description	Best responses for multi_start and pareto_set
Location	best_responses
Shape	2-dimensional: number of sets by number of responses
Type	Real
Scales	Dimension Type Label Contents Literal_contents 0 Integer set_ids set Ids false 1 String responses Response descriptors false